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Part of 1999 Irish Math Olympiad
Problems(2)
find all real numbers
Source: Ireland 1999
7/4/2009
Find all real numbers which satisfy: \frac{x^2}{(x\plus{}1\minus{}\sqrt{x\plus{}1})^2}<\frac{x^2\plus{}3x\plus{}18}{(x\plus{}1)^2}.
inequalities proposedinequalities
system of equations
Source: Ireland 1999
7/4/2009
Solve the system of equations:
y^2\equal{}(x\plus{}8)(x^2\plus{}2),
y^2\minus{}(8\plus{}4x)y\plus{}(16\plus{}16x\minus{}5x^2)\equal{}0.
algebrasystem of equationsalgebra proposed